The electrical operation of an object to be examined can be examined e.g. by measuring the magnetic field produced by the electric currents of the object using sensors placed outside the object. The modeling of a source distribution thus obtained based on the measured signals is, however, very difficult because each magnetic field distribution can be produced by many different source distributions. In other words, a source distribution cannot be solved unambiguously based on the measured signals, so to solve the problem, different restrictive conditions must be set, such as some parametric model based on prior information for a current, or a non-parametrised norm restriction.
For the non-parametrised modeling of a continuous current distribution, minimum norm estimates are usually used, in which there is an attempt to explain a signal measured using a multi-channel measurement device with a current distribution whose norm is as small as possible. As the norm, usually an L1 or L2 norm is selected, of which the previous is the sum of the lengths of the current elements over the selected volume, and the latter is the sum of the squares of the lengths of the current elements over the selected volume. The calculation of the minimum norm estimates has been described e.g. in publications “Interpreting magnetic fields of the brain: minimum norm estimates”, M. S. Hämäläinen et al, Medical & Biological Engineering & Computing, Vol. 32, pp. 35-42, 1994, as well as “Visualization of magnetoencephalographic data using minimum current estimates”, Uutela K. et al, NeuroImage, Vol. 10, pp. 173-180, 1999.
Conventional minimum norm estimates involve inherent problems such as slowness of calculation and susceptibility to noise. For example, in the case of an L2 norm, one needs an inverse matrix of matrix G, whose element (i, j) contains the inner product of the lead fields of the ith and jth measurement sensor, so one must calculate these inner products for each pair of sensors. The lead field is so determined that the signal measured by a sensor is the projection of the current distribution for the lead field of the sensor in question. The noise problems are due to the fact that matrix G calculated for the sensors is susceptible to noise, so in the calculation of its inverse matrix, regularisation is needed in the practical situations.
Regularisation methods, such as the truncation regularisation of the singular value decomposition, usually are non-intuitive, and usually also to be solved for each case specifically. A regularisation of the wrong type may lead to an erroneous modeling result.
Therefore, source modeling nowadays still involve problems such as the difficulty and slowness of the computation, the possible errors caused by noise, as well as the case-specificity due to the regularisation. Further, as stated above, the regularisation may cause considerable errors to the final computation result.